Quasi-Injective and Quasi-Projective Modules Over Hereditary Noetherian Prime Rings
Canadian journal of mathematics, Tome 26 (1974) no. 5, pp. 1173-1185

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The structure theory of hereditary noetherian prime (hnp) rings—in particular of Dedekind prime rings—has been recently developed by many authors including Eisenbud, Griffith, Michler and Robson; this theory extends some of the well-known results concerning commutative Dedekind domains. In this paper we study quasi-injective modules and quasi-projective modules over those (hnp) rings which are not right primitive and establish some results which extend the corresponding well-known results concerning commutative Dedekind domains. Let R be an (hnp) ring, which is not right primitive.
Singh, Surjeet. Quasi-Injective and Quasi-Projective Modules Over Hereditary Noetherian Prime Rings. Canadian journal of mathematics, Tome 26 (1974) no. 5, pp. 1173-1185. doi: 10.4153/CJM-1974-110-5
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[1] 1. Eisenbud, D. and Griffith, P., Serial Rings, J. Algebra 17 (1971), 389–400. Google Scholar

[2] 2. Eisenbud, D. and Robson, J. C., Modules over Dedekind prime rings, J. Algebra 16 (1970), 67–85. Google Scholar

[3] 3. Eisenbud, D. and Robson, J. C., Hereditary noetherian prime rings, J. Algebra 16 (1970), 86–104. Google Scholar

[4] 4. Faith, C. and Utumi, Y., Quasi injective modules and their endomorphism rings, Arch. Math. 15 (1964), 166–174. Google Scholar

[5] 5. Fuller, K. R., Generalized uniserial rings and their Kupisch series, Math. Z. 106 (1968), 248–260. Google Scholar

[6] 6. Golan, J. S., Characterizations of rings using quasi projective modules. II, Proc. Amer. Math. Soc. 28 (1971), 337–343. Google Scholar

[7] 7. Goldie, A. W., The structure of prime rings under ascending chain conditions, Proc. London Math. Soc. 8 (1958), 589–608. Google Scholar

[8] 8. Jacobson, N., The theory of rings, Mathematical Survey II (Amer. Math. Soc, Providence, 1943). Google Scholar

[9] 9. Johnson, R. E. and Wong, E. T., Quasi infective modules and irreducible rings, J. London Math. Soc. 36 (1961), 260–264. Google Scholar

[10] 10. Kupisch, H., Beitrage Zür Théorie nichtalbeinfacher Ringe mit minimal Bedingung, Crell J. 201 (1959), 100–112. Google Scholar

[11] 11. Matlis, E., Infective modules over noetherian rings, Pacific J. Math. 8 (1958), 511–528. Google Scholar

[12] 12. Michler, G. O., Characterisierung einer Klasse von Noetherschen Ringen, Math. Z. 100 (1967), 163–182. Google Scholar

[13] 13. Michlet, G. O., Structure of semi-perfect hereditary noetherian ring, J. Algebra 13 (1969), 327–344. Google Scholar

[14] 14. Miyashita, , On quazi infective modules, J. Fac. Sci. Hokkaido Univ. Ser. I 18 (1965), 158–187. Google Scholar

[15] 15. Murase, I., On the structure of generalized uniserial rings. I, Sci. Papers College Gen. Ed. Univ. Tokyo 13 (1963), 1–22. Google Scholar

[16] 16. Murase, I., On the structure of generalized uniserial rings, II, Sci. Papers College Gen. Ed. Tokyo 13 (1963), 131–158. Google Scholar

[17] 17. Murase, I., On the structure of generalized uniserial rings, III, Sci. Pap. Coll. Gen. Edu. Univ. Tokyo 14 (1964), 11–25. Google Scholar

[18] 18. Rangaswamy, K. M. and Vanaja, Quasi projectives in abelian categories, Pacific J. Math. 43 (1972) (to appear). Google Scholar

[19] 19. deRobert, E., Projectifs et injectifs, applications, C. R. Acad. Sci. Paris Ser. A-B 268 (1969), 361–364. Google Scholar

[20] 20. Wu, L. E. T. and Jans, J. P., On quasi projectives, Illinois. J. Math. 11 (1967), 439–447. Google Scholar

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